Publication date: Jan 2008
Abstract:
We apply a genetic algorithm method for selection of neutron star models relating them to the resonant models of the twin peak quasiperiodic oscillations observed in the X-ray neutron star binary systems. It was suggested that pairs of kilo-hertz peaks in the X-ray Fourier power density spectra of some neutron stars reflect a non-linear resonance between two modes of accretion disk oscillations. We investigate this concept for a specific neutron star source. Each neutron star model is characterized by the equation of state (EOS), rotation frequency Ω and central energy density ρc . These determine the spacetime structure governing geodesic motion and position dependent radial and vertical epicyclic oscillations related to the stable circular geodesics. Particular kinds of resonances (KR) between the oscillations with epicyclic frequencies, or the frequencies derived from them, can take place at special positions assigned ambiguously to the spacetime structure. The pairs of resonant eigenfrequencies relevant to those positions are therefore fully given by KR,ρc , Ω, EOS and can be compared to the observationally determined pairs of eigenfrequencies in order to eliminate the unsatisfactory sets (KR,ρc , Ω, EOS). For the elimination we use the advanced genetic algorithm. Genetic algorithm comes out from the method of natural selection when subjects with the best adaptation to assigned conditions have most chances to survive. The chosen genetic algorithm with sexual reproduction contains one chromosome with restricted lifetime, uniform crossing and genes of type 3/3/5. For encryption of physical description (KR,ρ, Ω, EOS) into chromosome we used Gray code. As a fitness function we use correspondence between the observed and calculated pairs of eigenfrequencies.
Authors:
Stuchlik, Zdenek; Urbanec, Martin; Török, Gabriel; Bakala, Pavel; Cermak, Petr;